{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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sfXpb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\nphy+Op7fwL/jxx5Kfzf+uLH2p/xfT/HH/9k=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image \n",
    "Image('../../../python_for_probability_statistics_and_machine_learning.jpg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Python for Probability, Statistics, and Machine Learning](https://www.springer.com/fr/book/9783319307152)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "from __future__ import division"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We saw with maximum likelihood estimation how we could use the\n",
    "principle of maximum likelihood to derive a formula of the data that\n",
    "would estimate the underlying parameters (say, $\\theta$). Under that\n",
    "method, the parameter was fixed, but unknown. If we change our\n",
    "perspective slightly and consider the underlying parameter as a random\n",
    "variable in its own right, this leads to additional flexibility in\n",
    "estimation.  This method is the simplest of the family of Bayesian\n",
    "statistical methods and is most closely related to maximum likelihood\n",
    "estimation. It is very popular in communications and signal processing\n",
    "and is the backbone of many important algorithms in those areas.\n",
    "\n",
    "Given that the parameter $\\theta$ is also a random variable, it has a\n",
    "joint distribution with the other random variables, say,\n",
    "$f(x,\\theta)$.  Bayes' theorem gives the following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{P}(\\theta|x) = \\frac{\\mathbb{P}(x|\\theta)\\mathbb{P}(\\theta)}{\\mathbb{P}(x)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The $\\mathbb{P}(x|\\theta)$ term is the usual likelihood term we have\n",
    "seen before. The term in the denominator is *prior* probability of the data $x$\n",
    "and it explicitly makes a very powerful claim: even before collecting or\n",
    "processing any data,  we know what the probability of that data is.  The $\\mathbb{P}(\\theta)$ is the prior probability of the\n",
    "parameter. In other words, regardless of the data that is collected, this is\n",
    "the probability of the parameter itself.\n",
    "\n",
    "In a particular application, whether or not you feel justified making these\n",
    "claims is something that you have to reconcile for yourself and the problem at\n",
    "hand.  There are many persuasive  philosophical arguments one way or the other,\n",
    "but the main thing to keep in mind when applying any method is whether or not\n",
    "the assumptions are reasonable for the problem at hand. \n",
    "\n",
    "However, for now, let's just assume that we somehow have $\\mathbb{P}(\\theta)$\n",
    "and the next step is the maximizing of this expression over the $\\theta$.\n",
    "Whatever results from that maximization is the maximum a-posteriori (MAP)\n",
    "estimator for $\\theta$. Because the maximization takes place with respect to\n",
    "$\\theta$ and not $x$, we can ignore the $\\mathbb{P}(x)$ part. To make things\n",
    "concrete, let us return to our original coin flipping problem.  From our\n",
    "earlier analysis, we know that the likelihood function for this problem is\n",
    "the following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\ell(\\theta) := \\theta^k (1-\\theta)^{ (n-k) }\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " where the probability of the coin coming up heads is $\\theta$. The\n",
    "next step is the prior probability, $\\mathbb{P}(\\theta)$. For this example, we\n",
    "will choose the $\\beta(6,6)$ distribution (shown in the top left panel of\n",
    "[Figure](#fig:MAP_001)). The $\\beta$ family of distributions is a gold mine\n",
    "because it allows for a wide variety of distributions using few input\n",
    "parameters. Now that we have all the ingredients, we turn to maximizing the\n",
    "posterior function, $\\mathbb{P}(\\theta|x)$. Because the logarithm is convex, we\n",
    "can use it to make the maximization process easier by converting the product to\n",
    "a sum without changing the extrema that we are looking for. Thus, we prefer the\n",
    "to work with the logarithm of $\\mathbb{P}(\\theta|x)$ as in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathcal{L} := \\log \\mathbb{P}(\\theta|x) =  \\log \\ell(\\theta) + \\log\\mathbb{P}(\\theta) - \\log\\mathbb{P}(x)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This is tedious to do by hand and therefore an excellent job\n",
    "for Sympy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(k + 5)/(n + 10)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    ">>> import sympy\n",
    ">>> from sympy import stats as st\n",
    ">>> from sympy.abc import p,k,n\n",
    "# setup objective function using sympy.log\n",
    ">>> obj=sympy.expand_log(sympy.log(p**k*(1-p)**(n-k)*\n",
    "                         st.density(st.Beta('p',6,6))(p)))\n",
    "# use calculus to maximize objective\n",
    ">>> sol=sympy.solve(sympy.simplify(sympy.diff(obj,p)),p)[0]\n",
    ">>> sol\n",
    "(k + 5)/(n + 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " which means that our MAP estimator of $\\theta$ is the following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\hat{\\theta}_{MAP} = \\frac{k+5}{n+10}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " where $k$ is the number of heads in the sample. This is obviously a\n",
    "biased estimator of $\\theta$,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}(\\hat{\\theta}_{MAP}) = \\frac{5+n \\theta}{10 +n} \\neq \\theta\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " But is this bias *bad*? Why would anyone want a biased estimator?\n",
    "Remember that we constructed this entire estimator using the idea of the prior\n",
    "probability of $\\mathbb{P}(\\theta)$ which *favors* (biases!) the estimate\n",
    "according to the prior.  For example, if $\\theta=1/2$, the MAP estimator\n",
    "evaluates to $\\hat{\\theta}_{MAP}=1/2$. No bias there! This is because the peak\n",
    "of the prior probability is at $\\theta=1/2$. \n",
    "\n",
    "To compute the corresponding variance for this estimator, we need this\n",
    "intermediate result,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{E}(\\hat{\\theta}_{MAP}^2) =\\frac{25 +10 n \\theta + n \\theta((n-1) p+1)}{(10+n)^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " which gives the following variance,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{V}(\\hat{\\theta}_{MAP}) = \\frac{n (1-\\theta) \\theta}{(n+10)^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's pause and compare this to our previous maximum likelihood (ML) estimator\n",
    "shown below:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\hat{\\theta}_{ML} = \\frac{1}{n} \\sum_{i=1}^n X_i =  \\frac{k}{n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " As we discussed before, the ML-estimator is unbiased with the\n",
    "following variance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{V}(\\hat{\\theta}_{ML}) = \\frac{\\theta(1-\\theta)}{n}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " How does this variance compare to that of the MAP? The ratio of the\n",
    "two is the following:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\frac{\\mathbb{V}(\\hat{\\theta}_{MAP})}{\\mathbb{V}(\\hat{\\theta}_{ML})}=\\frac{n^2}{(n+10)^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "  This ratio shows that the variance for the MAP-estimator is smaller\n",
    "than that of the the ML-estimator. This is payoff for having a biased\n",
    "MAP-estimator --- it requires fewer samples to estimate if the underlying\n",
    "parameter is consistent with the prior probability. If not, then it will take\n",
    "more samples to pull the estimator away from the bias. In the limit as $n\n",
    "\\rightarrow \\infty$, the ratio goes to one.  This means that the benefit of the\n",
    "reduced variance vanishes with enough samples. \n",
    "\n",
    "The above discussion admits a level of arbitrariness via the prior\n",
    "distribution. We don't have to choose just one prior, however. The\n",
    "following shows how we can use the previous posterior distribution as the\n",
    "prior for the next posterior distribution,"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathbb{P}(\\theta|x_{k+1}) = \\frac{\\mathbb{P}(x_{k+1}|\\theta)\\mathbb{P}(\\theta|x_k)}{\\mathbb{P}(x_{k+1})}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " This is a very different strategy because we are using every data\n",
    "sample $x_k$ as a parameter for the posterior distribution instead of lumping\n",
    "all the samples together in a summation (this is where we got the $k$\n",
    "term in the prior case). This case is much harder to analyze because now\n",
    "every incremental posterior distribution is itself a random function because of\n",
    "the injection of the $x$ random variable. On the other hand, this is more in\n",
    "line with more general Bayesian methods because it is clear that the output of\n",
    "this estimation process is a posterior distribution function, not just a single\n",
    "parameter estimate. \n",
    "\n",
    "[Figure](#fig:MAP_001) illustrates this method. The graph\n",
    "in the top row, far left shows the prior probability ($\\beta(6,6)$) and the dot\n",
    "on the top shows the most recent MAP-estimate for $\\theta$. Thus, before we\n",
    "obtain any data, the peak of the prior probability  is the estimate. The next\n",
    "graph to right shows the effect of $x_0=0$ on the incremental prior\n",
    "probability.  Note that the estimate has barely moved to the left. This is\n",
    "because the influence of the data has not caused the prior probability to drift\n",
    "away from the original $\\beta(6,6)$-distribution.  The first two rows of the\n",
    "figure all have $x_k=0$ just to illustrate how far left the original prior\n",
    "probability can be moved by those data. The dots on the tops of the sub-graphs\n",
    "show how the MAP estimate changes frame-by-frame as more data is incorporated.\n",
    "The remaining graphs, proceeding top-down, left-to-right show the incremental\n",
    "change in the prior probability for $x_k=1$.  Again, this shows how far to the right \n",
    "the estimate can be pulled from where it started. For this example, there\n",
    "are an equal number of $x_k=0$ and $x_k=1$ data, which corresponds \n",
    "to $\\theta=1/2$.  \n",
    "\n",
    "<!-- dom:FIGURE: [fig-statistics/MAP_001.png, width=500 frac=0.95] The prior probability is the $\\beta(6,6)$ distribution shown in the top left panel. The dots near the peaks of each of the subgraphs indicate the MAP estimate at that frame <div id=\"fig:MAP_001\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:MAP_001\"></div>\n",
    "\n",
    "<p>The prior probability is the $\\beta(6,6)$ distribution shown in the top left panel. The dots near the peaks of each of the subgraphs indicate the MAP estimate at that frame</p>\n",
    "<img src=\"fig-statistics/MAP_001.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "**Programming Tip.**\n",
    "\n",
    "Although the IPython Notebook accompanying this section has the full source\n",
    "code, the following is a quick paraphrase of how [Figure](#fig:MAP_001) was\n",
    "constructed. The first step is to recursively create the\n",
    "posteriors from the data. Note the example data is sorted\n",
    "to make the progression easy to see as a sequence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy.abc import p,x\n",
    "from sympy.stats import density, Beta, Bernoulli\n",
    "prior = density(Beta('p',6,6))(p)\n",
    "likelihood=density(Bernoulli('x',p))(x)\n",
    "data = (0,0,0,0,0,0,0,1,1,1,1,1,1,1,1)\n",
    "posteriors = [prior]\n",
    "for i in data:\n",
    "    posteriors.append(posteriors[-1]*likelihood.subs(x,i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " With the posteriors in hand, the next step \n",
    "is to compute the peak values at each frame using the\n",
    "`fminbound` function from Scipy's  `optimize` module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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9tGe7du0SbNFKS6ZMmYKtW7fSVK+IiouLceHCBYwcOVLwtv39/VFVVUUbOEigrKwMubm5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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fc13470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import fminbound\n",
    "\n",
    "fig,ax = subplots(4,4,sharex=True,\n",
    "                  subplot_kw={'yticks':[''],\n",
    "                              'yticklabels':[''],\n",
    "                              'xticks':[0,0.5,1],\n",
    "                              'xticklabels':[0,0.5,1]})\n",
    "fig.set_size_inches((8,8))\n",
    "pvals = linspace(0,1,100)\n",
    "mxvals = []\n",
    "for i,j in zip(ax.flat,posteriors):\n",
    "    i.plot(pvals, sympy.lambdify(p,j)(pvals),color='k')\n",
    "    mxval = fminbound(sympy.lambdify(p,-j),0,1)\n",
    "    mxvals.append(mxval)\n",
    "    h = i.axis()[-1]\n",
    "    i.axis(ymax=h*1.3)\n",
    "    i.plot(mxvals[-1],h*1.2,'ok')\n",
    "    i.plot(mxvals[:-1],[h*1.2]*len(mxvals[:-1]),'o',color='gray',alpha=.3)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [Figure](#fig:MAP_002) is the same as [Figure](#fig:MAP_001) except that\n",
    "the initial prior probability is the $\\beta(1.3,1.3)$-distribution, which has a\n",
    "wider lobe that the $\\beta(6,6)$-distribution. As shown in the figure, this\n",
    "prior has the ability to be swayed more violently one way or the other based on\n",
    "the $x_k$ data that is incorporated. This means that it can more quickly adapt\n",
    "to data that is not so consistent with the initial prior and thus does not\n",
    "require a large amount of data in order to *unlearn* the prior probability.\n",
    "Depending on the application, the ability to unlearn the prior probability or\n",
    "stick with it is a design problem for the analyst. In this example, because the\n",
    "data are representative of a $\\theta=1/2$ parameter, both priors eventually\n",
    "settle on an estimated posterior that is about the same. However, if this had\n",
    "not been the case ($\\theta \\neq 1/2$), then the second prior \n",
    "would have produced a better estimate for the same amount of data [^IPyNote]. \n",
    "\n",
    "[^IPyNote]: The IPython Notebook corresponding to this\n",
    "chapter contains the source code sot hat you can try different\n",
    "combinations of priors and data values.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-statistics/MAP_002.png, width=500 frac=0.95] For this example, the prior probability is the $\\beta(1.3,1.3)$ distribution, which has a wider main lobe than the $\\beta(6,6)$ distribution. The dots near the peaks of each of the subgraphs indicate the MAP estimate at that frame. <div id=\"fig:MAP_002\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:MAP_002\"></div>\n",
    "\n",
    "<p>For this example, the prior probability is the $\\beta(1.3,1.3)$ distribution, which has a wider main lobe than the $\\beta(6,6)$ distribution. The dots near the peaks of each of the subgraphs indicate the MAP estimate at that frame.</p>\n",
    "<img src=\"fig-statistics/MAP_002.png\" width=500>\n",
    "\n",
    "<!-- end figure -->\n",
    "\n",
    "\n",
    "Because we have the entire posterior density available, we can compute\n",
    "something that is closely related to the confidence interval we discussed\n",
    "earlier, except in this situation, given the Bayesian interpretation, it is\n",
    "called a *credible interval* or *credible set*.  The idea is that we want to\n",
    "find a symmetric interval around the peak that accounts for 95% (say) of the\n",
    "posterior density. This means that we can then say the probability that the\n",
    "estimated parameter is within the credible interval is 95%. The computation\n",
    "requires significant numerical processing because even though we have the\n",
    "posterior density in hand, it is hard to integrate analytically and requires\n",
    "numerical quadrature (see Scipy's `integrate` module).  [Figure](#fig:MAP_003)\n",
    "shows extent of the interval and the shaded region under the posterior density\n",
    "that accounts for 95%.\n",
    "\n",
    "<!-- dom:FIGURE: [fig-statistics/MAP_003.png, width=500 frac=0.75] The *credible interval* in Bayesian maximum a-posteriori is the interval corresponding to the shaded region in the posterior density.  <div id=\"fig:MAP_003\"></div> -->\n",
    "<!-- begin figure -->\n",
    "<div id=\"fig:MAP_003\"></div>\n",
    "\n",
    "<p>The <em>credible interval</em> in Bayesian maximum a-posteriori is the interval corresponding to the shaded region in the posterior density.</p>\n",
    "<img src=\"fig-statistics/MAP_003.png\" width=500>\n",
    "\n",
    "<!-- end figure -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.abc import p,x\n",
    "prior = density(Beta('p',1.3,1.3))(p)\n",
    "# prior = density(Beta('p',6,6))(p)\n",
    "likelihood=density(Bernoulli('x',p))(x)\n",
    "data = (0,0,0,0,0,0,0,1,1,1,1,1,1,1,1)\n",
    "posteriors = [prior]\n",
    "for i in data:\n",
    "    posteriors.append(posteriors[-1]*likelihood.subs(x,i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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dEnmBu7s7Dh8+jOzsbAQHB+vUSmwqphJBswLabdy4cejfvz86d+6Mx48fixaH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fc13588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = subplots(4,4,sharex=True,\n",
    "                  subplot_kw={'yticks':[''],\n",
    "                              'yticklabels':[''],\n",
    "                              'xticks':[0,0.5,1],\n",
    "                              'xticklabels':[0,0.5,1]})\n",
    "fig.set_size_inches((8,8))\n",
    "pvals = linspace(0,1,100)\n",
    "mxvals = []\n",
    "for i,j in zip(ax.flat,posteriors):\n",
    "    i.plot(pvals, sympy.lambdify(p,j)(pvals),color='k')\n",
    "    mxval = fminbound( sympy.lambdify(p,-j),0,1)\n",
    "    mxvals.append(mxval)\n",
    "    h = i.axis()[-1]\n",
    "    i.axis(ymax=h*1.3)\n",
    "    i.plot(mxvals[-1],h*1.2,'ok')\n",
    "    i.plot(mxvals[:-1],[h*1.2]*len(mxvals[:-1]),'o',color='gray',alpha=.3)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
